Rather little is known about the very general notion of higher topos theory. A rich theory however exists in the context of (∞,1)-categories, as described in Jacob Lurie's book Higher Topos Theory, which only covers the (∞,1)(\infty, 1) case.

Just as the archetypical example of an ordinary topos (i.e. a (1,1)(1,1)-topos) is Set – the category of 0-categories – so the ∞\infty-category of n-categories or at least of nn-groupoids should form the archetypical example of an (n+1,1)(n+1,1)-topos.